Method for estimating phase error in MIMO OFDM communications system

ABSTRACT

A method for estimating a phase error existing in a receiver of a MIMO OFDM communications system is disclosed. The method includes executing Hermitian transpose on channel coefficient matrix of the MIMO OFDM communications system for generating Hermitian-transposed channel coefficient matrix, multiplying received signal matrix of the receiver with the Hermitian-transposed channel coefficient matrix for generating converted signals, summing products of the converted signals and complex conjugates of pilot signals corresponding to the converted signals for generating a sum result, and generating the phase error according to the sum result, the converted signals, and the complex conjugates of the pilot signals. The pilot signals are extracted from the received signal matrix.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 12/346,886filed on Dec. 31, 2008, entitled “Method for estimating phase error inMIMO OFDM communications system,” which is hereby incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for estimating phase error inMIMO OFDM communications system, and more particularly, to a method forestimating phase error existing in the receiver of the MIMO OFDMcommunications system.

2. Description of the Prior Art

Please refer to FIG. 1. FIG. 1 is a diagram illustrating a conventionalMultiple Input Multiple Output (MIMO) Orthogonal Frequency DivisionMultiplexing (OFDM) communications system 100. It is noted that the MIMOOFDM communication system here includes Multiple Input Single Output(MISO) OFDM communication system, for example, a 2T1R OFDM system, i.e.the number of the transmitting antennas T_(X) is 2, and the number ofthe receiving antennas R_(X) is 1.

The MIMO OFDM communications system 100 comprises a transmitter 110 fortransmitting radio frequency signals and a receiver 120 for receivingradio frequency signals from the transmitter 110.

The transmitter 110 comprises a modulation device 111, aspace-time-frequency processing device 112, a transmitting signaltransforming module 116, and a plurality of transmitting antennas T_(X).

The transmitting signal transforming module 116 comprises an InverseFast Fourier Transform (IFFT) device 113, a Digital/Analog Converter(DAC) 114, and an RF (radio frequency) circuit 115.

The modulation device 111 is disposed for modulating data. Thespace-time-frequency processing device 112 is coupled to the modulationdevice 111 and disposed for processing the modulated data. Thetransmitting signal transforming module 116 is coupled between thespace-time-frequency processing device 112 and the transmitting antennasT_(X) for receiving the processed data from the space-time-frequencyprocessing device 112 and transforming the received data to radiofrequency signals to the transmitting antennas T_(X). More particularly,in the transmitting signal transforming module 116, the IFFT device 113is coupled to the space-time-frequency processing device 112 anddisposed for executing IFFT on the processed modulated data andaccordingly outputting transformed data; the DAC 114 is coupled to theIFFT device 113 and disposed for converting the transformed data toanalog signals; the RF circuit 115, coupled to the DAC 114, receives theanalog signals and accordingly up-converts the received analog signalsto radio frequency signals. The antennas T_(X), coupled to the RFcircuit 115 of the transmitting signal transforming module 116, receivesthe radio frequency signals from the RF circuit 115 and transmits thereceived radio frequency signals.

The receiver 120 comprises a plurality of receiving antennas R_(X), areceiving signal transforming module 130, a timing/phase compensationdevice 123, an equalizer 124, a demodulation device 125, and a PhaseLock Loop (PLL) 126.

The receiving signal transforming module 130 comprises an RF circuit127, an Analog/Digital Converter (ADC) 121, and an FFT device 122.

The receiving antennas R_(X) receive the radio frequency signalstransmitted from the transmitting antennas T_(X) of the transmitter 110.The receiving signal transforming module 130 is coupled between thereceiving antennas R_(X) for receiving the radio frequency signals andtransforming the received radio frequency signals to transformed signalsto the time/phase compensation device 123. More particularly, in thereceiving signal transforming module 130, the RF circuit 127, coupled tothe receiving antennas R_(X), down-converts the radio frequency signalsreceived from the receiving antennas R_(X), i.e., a plurality ofreceiving paths, to base band or intermediate band analog signals; theADC 121, coupled to the RF circuit 127, converts the analog signals fromthe RF circuit 127 to digital signals; the FFT device 122, coupled tothe ADC 121, executes FFT on the digital signals received from the ADC121 and accordingly outputs transformed signals. The timing/phasecompensation device 123, coupled to the FFT device 122 of the receivingsignal transforming module 130, compensates the transformed signalsaccording to the phase outputted from the PLL 126. The equalizer 124,coupled to the timing/phase compensation device 123, the demodulationdevice 125, and the PLL 126, equalizes the compensated signals from thetiming/phase compensation device 123 and accordingly outputs to thedemodulation device 125, and estimates phase error θ of the receivedcompensated signals and outputs the estimated phase error θ to the PLL126. The PLL 126, coupled to the equalizer 124, receives the phase errorθ and accordingly adjusts its phase, and outputs a clock signal with theadjusted phase to the timing/phase compensation device 123. Thedemodulation device 125, coupled to the equalizer 124, demodulates theequalized signals and accordingly outputs data.

Because of frequency mismatch, timing drift or Common Phase Error (CPE),a phase error θ exists between the actual received signal and thecorrect signal. Therefore, in data tones, the equalizer 124 is utilizedto estimate the phase error θ of the received signal and accordinglyoutputs the estimated phase error θ to the PLL 126 since the data signalcan be extracted from the received radio frequency signal. Consequently,the PLL 126 enables the timing/phase compensation device 123 tocorrectly compensate the timing/phase of the received signals. Theequalizer 124 can be a zero-forcing (ZF) equalizer.

Assuming the number of the transmitting antennas T_(X) is 2, and thenumber of the receiving antennas R_(X) is 3 (a 2T3R OFDM communicationssystem), therefore, the received signals (after being fast Fouriertransformed) can be derived from the following equations:

$\begin{matrix}{{\left\lbrack {y_{1,t}\mspace{25mu} y_{1,{t + 1}}} \right\rbrack = {{\left\lbrack {h_{11}\mspace{11mu} h_{12}} \right\rbrack \begin{bmatrix}{x_{1}^{j\theta}} & {x_{2}^{j\theta}} \\{{- x_{2}^{*}}^{j\theta}} & {x_{1}^{*}^{j\theta}}\end{bmatrix}} + \left\lbrack {n_{1,t}\mspace{20mu} n_{1,{t + 1}}} \right\rbrack}};} & (1) \\{{\left\lbrack {y_{2,t}\mspace{25mu} y_{2,{t + 1}}} \right\rbrack = {{\left\lbrack {h_{21}\mspace{11mu} h_{22}} \right\rbrack \begin{bmatrix}{x_{1}^{j\theta}} & {x_{2}^{j\theta}} \\{{- x_{2}^{*}}^{j\theta}} & {x_{1}^{*}^{j\theta}}\end{bmatrix}} + \left\lbrack {n_{{2,t}\mspace{14mu}}n_{2,{t + 1}}} \right\rbrack}};} & (2) \\{{\left\lbrack {y_{3,t}\mspace{25mu} y_{3,{t + 1}}} \right\rbrack = {{\left\lbrack {h_{31}\mspace{11mu} h_{32}} \right\rbrack \begin{bmatrix}{x_{1}^{j\theta}} & {x_{2}^{j\theta}} \\{{- x_{2}^{*}}^{j\theta}} & {x_{1}^{*}^{j\theta}}\end{bmatrix}} + \left\lbrack {n_{3,t}\mspace{14mu} n_{3,{t + 1}}} \right\rbrack}};} & (3) \\{ \begin{matrix}{Y_{61} = \begin{bmatrix}y_{1,t} \\* \\y_{1,{t + 1}} \\y_{2,t} \\* \\y_{2,{t + 1}} \\y_{3,t} \\* \\y_{3,{t + 1}}\end{bmatrix}_{61}} \\{= {}{{H_{62}X_{21}} + N_{61}}} \\{= \begin{bmatrix}h_{11} & {- h_{12}} \\h_{12}^{*} & {+ h_{11}^{*}} \\h_{21} & {- h_{22}} \\h_{22}^{*} & {+ h_{21}^{*}} \\h_{31} & {- h_{32}} \\h_{32}^{*} & {+ h_{31}^{*}}\end{bmatrix}_{6 \times 2}} \\{{\begin{bmatrix}{x_{1}^{j\theta}} \\{x_{2}^{*}^{j\theta}}\end{bmatrix}_{2 \times 1} +}} \\{{\begin{bmatrix}n_{1,t} \\n_{1,{t + 1}}^{*} \\n_{2,t} \\n_{2,{t + 1}}^{*} \\n_{3,t} \\n_{3,{t + 1}}^{*}\end{bmatrix}_{6 \times 1};}}\end{matrix}} & (4) \\\begin{matrix}{G_{26} = {{pinv}(H)}} \\{= {\left( {H_{62}^{H} \cdot H_{62}} \right)^{- 1} \cdot H_{6 \times 2}^{H}}} \\{= {\frac{1}{\sum\limits_{i = {1:3}}{\sum\limits_{j = {1:2}}h_{ij}^{2}}} \cdot}} \\{{\begin{bmatrix}{+ h_{11}^{*}} & {+ h_{12}} & {+ h_{21}^{*}} & {+ h_{22}} & h_{31}^{*} & {+ h_{32}} \\{- h_{12}^{*}} & {+ h_{11}} & {- h_{22}^{*}} & {+ h_{21}} & {- h_{32}^{*}} & {+ h_{31}}\end{bmatrix};}}\end{matrix} & (5) \\{{X_{21} = {\begin{bmatrix}{x_{1}^{j\theta}} \\{x_{2}^{*}^{j\theta}}\end{bmatrix} = {{G_{26}Y_{61}} + N_{21}}}};} & (6)\end{matrix}$

where * represents the complex conjugate of the corresponding symbol(each symbol in the equations (1)˜(6) are complex numbers), X_(2×1)represents the data signal matrix, Y_(6×1) represents the receivedsignal matrix after being fast Fourier transformed, H represents thechannel coefficient matrix, G_(2×6) represents the gain matrix, N_(2×1)represents the noise matrix, H^(H) represents the Hermitian transpose ofthe channel coefficient matrix H, each element h_(ij) in the matrix Hrepresents the channel coefficient between one transmitting antenna andone receiving antenna, n_(j) and n_(j,t+1) represent noise, y_(i,t) andy_(i,t+1) represents the received signals from the i^(th) receivingantennas R_(X) after being fast Fourier transformed, and x_(j)represents the data signal. Therefore, in data tone, the equalizer 124can estimate the phase error θ according to the equations (1)˜(6). ThePLL 126 adjusts its phase according to the estimated phase error θ andenables the timing/phase compensation device 123 to correctly compensatethe timing/phase of the received signals.

However, in the equation (6), the value of the gain of the gain matrix Gis not relatively large enough (compared to the noise), and thus thenoise matrix N cannot be ignored, which affects the accuracy of theestimation of the phase error θ.

Furthermore, in the MIMO OFDM communications system, the number of thereceiving antennas has to be larger than the number of the transmittingantennas. In other words, the number of the receiving antennas cannot beless than the number of the transmitting antennas. Assuming the numberof the transmitting antennas T_(X) is 2, and the number of the receivingantennas R_(X) is 1 (a 2T1R OFDM communications system), therefore, thereceived signals can be derived from the following equations:

$\begin{matrix}{{y_{1} = {{\left\lbrack {h_{11\mspace{11mu}}h_{12}} \right\rbrack \begin{bmatrix}{x_{1}^{j\theta}} \\{x_{2}^{j\theta}}\end{bmatrix}} = {{\left( {{h_{11}x_{1}} + {h_{12}x_{2}}} \right)e^{j\theta}} + {noise}}}};} & (7)\end{matrix}$

where y₁ represents the received signal after being fast Fouriertransformed, x₁ and x₂ represent the pilot signals, h₁₁ and h₁₂represent the channel coefficients. If x₁=1, x₂=−1, and h₁₁ and h₁₂ arealmost the same, in this condition, the received signal y₁ approximatelyequals the noise, and consequently the phase error θ cannot beestimated, which is why in the MIMO OFDM communications system, thenumber of the receiving antennas has to be larger than the number of thetransmitting antennas.

SUMMARY OF THE INVENTION

The present invention provides a receiver of a Multiple Input MultipleOutput (MIMO) Orthogonal Frequency Division Multiplexing (OFDM)communications system. The receiver comprises at least one receivingantenna for receiving radio frequency signals from at least onereceiving paths, wherein a pilot signal is extracted from each of thereceived radio frequency signals, a receiving signal transforming modulecoupled to the at least one receiving antenna for receiving the radiofrequency signals and generating transformed signals accordingly, asignal converting device coupled to the receiving signal transformingmodule for converting the received transformed signals to convertedsignals, and a signal summation device coupled to the signal convertingdevice for summing products of the converted signals and complexconjugates of pilot signals corresponding to the converted signals andaccordingly generating a sum result, and a Phase Lock Loop (PLL) coupledto the signal summation device, estimating a phase error according tothe sum result, the converted signals, and the complex conjugates of thepilot signals.

The present invention further provides a method for estimating a phaseerror existing in a receiver of a MIMO OFDM communications system. Themethod comprises executing Hermitian transpose on channel coefficientmatrix of the MIMO OFDM communications system for generatingHermitian-transposed channel coefficient matrix, multiplying receivedsignal matrix of the receiver with the Hermitian-transposed channelcoefficient matrix for generating converted signals, summing products ofthe converted signals and complex conjugates of pilot signalscorresponding to the converted signals for generating a sum result,wherein the pilot signals are extracted from the received signal matrix,and generating the phase error according to the sum result, theconverted signals, and the complex conjugates of the pilot signals.

The present invention further provides a method for estimating a phaseerror in a receiver of a MIMO OFDM communications system. The methodcomprises executing Hermitian transpose on a channel coefficient matrixof the MIMO OFDM communications system for generating aHermitian-transposed channel coefficient matrix; multiplying theHermitian-transposed channel coefficient matrix with the channelcoefficient matrix for generating a product channel coefficient matrix;adding a real constant to each element on diagonal of the productchannel coefficient matrix for generating a constant-added productchannel coefficient matrix; inversing the constant-added product channelcoefficient matrix for generating an inversed constant-added productchannel coefficient matrix; multiplying the inversed constant-addedproduct channel coefficient matrix with the Hermitian-transposed channelcoefficient matrix for generating a diversity gain matrix; andgenerating the phase error according to the diversity gain matrix, areceived signal matrix, and a pilot signal matrix.

These and other objectives of the present invention will no doubt becomeobvious to those of ordinary skill in the art after reading thefollowing detailed description of the preferred embodiment that isillustrated in the various figures and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a conventional MIMO OFDM communicationssystem.

FIG. 2 is a diagram illustrating an MIMO OFDM communications systemaccording to a first embodiment of the present invention.

FIG. 3 is a flowchart illustrating a method for estimating phase erroraccording to the first embodiment of the present invention.

FIG. 4 is a flowchart illustrating a method for estimating phase erroraccording to a second embodiment of the present invention.

DETAILED DESCRIPTION

Please refer to FIG. 2. FIG. 2 is a diagram illustrating an MIMO OFDMcommunications system 200 according to a first embodiment of the presentinvention.

The MIMO OFDM communications system 200 comprises a transmitter 110 fortransmitting radio frequency signals and a receiver 220 for receivingradio frequency signals from the transmitter 110.

The transmitter 110 functions as the same in the conventional MIMO OFDMcommunications system 100 and the related description is omitted.

The receiver 220 comprises a plurality of receiving antennas R_(X), areceiving signal transforming module 230, a timing/phase compensationdevice 223, an equalizer 224, a demodulation device 225, a PLL 226, asignal converting device 227, and a signal summation device 228.

The receiving signal transforming module 230 comprises an RF circuit229, an ADC 221, and an FFT device 222.

The receiving antennas R_(X) receive the radio frequency signalstransmitted from the transmitting antennas T_(X) of the transmitter 110.The receiving signal transforming module 230 is coupled between thereceiving antennas R_(X) and the time/phase compensation device 223 forreceiving the radio frequency signals and transforming the receivedsignals to transformed signals to the time/phase compensation device223. More particularly, in the receiving signal transforming module 230,the RF circuit 229 receives the radio frequency signals from thereceiving antennas R_(X) and down-converts the received radio frequencysignals to base band or intermediate band analog signals; the ADC 221,coupled to the RF circuit 229, converts the analog signals received fromthe RF circuit 229 to digital signals; the FFT device 222, coupled tothe ADC 221, executes FFT on the received digital signals from the ADC221 and accordingly outputs transformed signals. The timing/phasecompensation device 223, coupled to the FFT device 222 of the receivingsignal transforming module 230, compensates the transformed signalsaccording to the phase outputted from the PLL 226. The PLL 226, coupledto the signal summation device 228, estimates the phase error θ, andaccordingly adjusts its phase to output a clock signal with the adjustedphase to the timing/phase compensation device 223. The equalizer 224,coupled between the timing/phase compensation device 223 and thedemodulation device 225, equalizes the compensated signals from thetiming/phase compensation device 223. The demodulation device 225,coupled to the equalizer 224, demodulates the equalized signals andaccordingly outputs data.

In pilot tone, the signal converting device 227, the signal summationdevice 228, and the PLL 226 are utilized to estimate the phase error θof the received signal y (after being fast Fourier transformed).Therefore, the clock signal with the adjusted phase outputted from thePLL 226 enables the timing/phase compensation device 223 to correctlycompensate the timing/phase of the received signal y.

The signal converting device 227 is coupled between the FFT device 222and the signal summation device 228. The signal summation device 228 iscoupled between the signal converting device 227 and the PLL 226.

The signal converting device 227 executes Hermitian transpose on thechannel coefficient matrix H and multiplies the transposed matrix H^(H)with the received signal y. Therefore, the signal converting device 227generates converted signal x′ according to the received signal y, andthe channel coefficient matrix H.

The signal summation device 228 sums all of the products of eachconverted signal x′ and the complex conjugate of its corresponding pilotsignal x.

The PLL 226 estimates the phase error θ according to the sum result ofthe signal summation device 228, the converted signal x′, and thecomplex conjugates of the pilot signal x.

Assuming the number of the transmitting antennas T_(X) is 2, and thenumber of the receiving antennas R_(X) is 2 (a 2T2R OFDM communicationssystem), therefore, the received signal y (after being fast Fouriertransformed) can be derived from the following equations:

$\begin{matrix}{{Y_{21} = {\begin{pmatrix}y_{1} \\y_{2}\end{pmatrix} = {{{H_{22} \cdot X_{21}} + N_{21}} = {{\begin{pmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{pmatrix}\begin{pmatrix}{x_{1}^{j\theta}} \\{x_{2}^{j\theta}}\end{pmatrix}} + \begin{pmatrix}n_{1} \\n_{2}\end{pmatrix}}}}};} & (8)\end{matrix}$

where Y_(2×1) represents the received signal matrix after being fastFourier transformed, H_(2×2) represents the channel coefficient matrix,X_(2×1) represents the pilot signal matrix, and N_(2×1) represents thenoise matrix;the signal converting device 227 executes Hermitian transpose on thechannel coefficient matrix H, and multiplies the received signal Y,which derives the following equation (ignoring the noise matrixN_(2×1)):

$\begin{matrix}\begin{matrix}{\begin{pmatrix}x_{1}^{\prime} \\x_{2}^{\prime}\end{pmatrix} = {H_{22}^{H} \cdot Y_{21}}} \\{= {\begin{pmatrix}h_{11}^{*} & h_{21}^{*} \\h_{12}^{*} & h_{22}^{*}\end{pmatrix}\begin{pmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{pmatrix}\begin{pmatrix}{x_{1}^{j\theta}} \\{x_{2}^{j\theta}}\end{pmatrix}}} \\{{= \begin{pmatrix}{{\left( {{h_{11}}^{2} + {h_{21}}^{2}} \right)x_{1}^{j\theta}} + {\left( {{h_{11}^{*}h_{12}} + {h_{21}^{*}h_{22}}} \right)x_{2}^{j\theta}}} \\{{\left( {{h_{12}}^{2} + {h_{22}}^{2}} \right)x_{1}^{j\theta}} + {\left( {{h_{12}^{*}h_{11}} + {h_{22}^{*}h_{21}}} \right)x_{1}^{j\theta}}}\end{pmatrix}};}\end{matrix} & (9)\end{matrix}$

the signal summation device 228 sums the products of x₁′x₁* and x₂′x₂*and accordingly generates the following equation:

$\begin{matrix}\begin{matrix}{{{x_{1}^{\prime}x_{1}^{*}} + {x_{2}^{\prime}x_{2}^{*}}} = {{\left( {{h_{11}}^{2} + {h_{21}}^{2}} \right){x_{1}}^{2}^{j\theta}} + {\left( {{h_{12}}^{2} + {h_{22}}^{2}} \right){x_{2}}^{2}^{j\theta}} +}} \\{{{\left( {{h_{11}^{*}h_{12}} + {h_{21}^{*}h_{22}}} \right)x_{2}x_{1}^{*}^{j\theta}} +}} \\{{\left( {{h_{12}^{*}h_{11}} + {h_{22}^{*}h_{21}}} \right)x_{1}x_{2}^{*}^{j\theta}}} \\{= \left\{ {{\left( {{h_{11}}^{2} + {h_{21}}^{2}} \right){x_{1}}^{2}} + {\left( {{h_{12}}^{2} + {h_{22}}^{2}} \right){x_{2}}^{2}} +} \right.} \\{\left. {2\mspace{11mu} R\; {e\;\left\lbrack {\left( {{h_{11}^{*}h_{12}} + {h_{21}^{*}h_{22}}} \right)x_{2}x_{1}^{*}} \right\rbrack}} \right\} ^{j\theta}} \\{{= {C\; ^{j\theta}}};}\end{matrix} & (10)\end{matrix}$

where Re [(h₁₁*h₁₂+h₂₁*h₂₂)x₂x₁] represents the real part of[(h₁₁*h₁₂+h₂₁*h₂₂) x₂x₁], and C represents{(|h₁₁|²+|h₂₁|²)|x₁|²+(|h₁₂|²+|h₂₂|²)|x₂|²+2Re[h₁₁*h₁₂+h₂₁*h₂₂)x₂x₁*]},which is a real value.

In the equation (9), because the received signals y₁ and y₂ are known,and the channel coefficients h₁₁, h₁₂, h₂₁, and h₂₂ are known, theconverted signals x₁′ and x₂′ can be derived.

Since the result generated from the signal summation device 228 is largeenough to ignore the noise matrix N_(2×1), the phase error θ can beeasily derived from the equation (10). In other words, in the equation(10), the term (Ce^(jθ)+noise) should be instead of the term Ce^(jθ).However, the constant C is so much larger than the noise term that thenoise term can be ignored. Therefore, the phase error θ can be estimatedfrom the tangent of “x₁′x₁*+x₂′x₂*”. For example, if “x₁′x₁*+x₂′x₂*”equals to (1+j1), the tangent of “x₁′x₁*+x₂′x₂*” is 1, and thus, thephase error θ equals to 45°. Therefore, the PLL 226 can efficientlyestimate the phase error θ. The PLL 226 then adjusts its phase accordingto the estimated phase error θ (for example, 45°) and enables thetiming/phase compensation device 223 to correctly compensate thetiming/phase of the received signal.

Please refer to FIG. 3. FIG. 3 is a flowchart illustrating a method 300for estimating phase error according to the first embodiment of thepresent invention. The steps of the method 300 are described as follows:

Step 301: Executing Hermitian transpose on the channel coefficientmatrix H for generating a Hermitian-transposed channel coefficientmatrix H_(A);

Step 302: Multiplying the received signals y with theHermitian-transposed channel coefficient matrix H_(A) for generating theconverted signals x′;

Step 303: Summing all products of each of the converted signal x′ andthe corresponding pilot signal x; and

Step 304: Generating the phase error θ according to the summation fromthe step 303.

Steps 303 and 304 have to be done in the pilot tone of the MIMO OFDMcommunications system 200 since the pilot signal x is only known in thepilot tone.

According to the first embodiment of the present invention, the MIMOOFDM system can comprises receiving antennas whose number is less thanthe number of the transmitting antenna. For example, assuming the numberof the transmitting antennas T_(X) is 2, and the number of the receivingantennas R_(X) is 1 (a 2T1R OFDM communications system), therefore, thereceived signals can be derived from the following equations:

$\begin{matrix}{y_{1} = {{\left\lbrack {h_{11}\mspace{14mu} h_{12}} \right\rbrack \begin{bmatrix}{x_{1}^{j\theta}} \\{x_{2}^{j\theta}}\end{bmatrix}} = {{\left( {{h_{11}x_{1}} + {h_{12}x_{2}}} \right)^{j\theta}} + {{noise}.}}}} & (11)\end{matrix}$

According to the steps 301 and 302, the received signal y₁ multiplieswith the Hermitian-transposed channel coefficient matrix H_(A) andaccordingly the converted signals x₁′ and x₂′ are generated, andaccording to the step 303, the products of x₁′x₁* and x₂′x₂* are summed,which is disclosed as the following equations:

$\begin{matrix}{{{x_{1}^{\prime}x_{1}^{*}} = {{h_{11}^{*}x_{1}^{*}y_{1}} = {\left( {{{h_{11}}^{2}{x_{1}}^{2}} + {h_{11}^{*}h_{12}x_{2}x_{1}^{*}}} \right)^{j\theta}}}};} & (12) \\{{{x_{2}^{\prime}x_{2}^{*}} = {{h_{12}^{*}x_{2}^{*}y_{1}} = {\left( {{{h_{12}}^{2}{x_{2}}^{2}} + {h_{12}^{*}h_{11}x_{1}x_{2}^{*}}} \right)^{j\theta}}}};\mspace{14mu} {and}} & (13) \\\begin{matrix}{{{x_{1}^{\prime}x_{1}^{*}} + {x_{2}^{\prime}x_{2}^{*}}} = {\left( {{{h_{11}}^{2}{x_{1}}^{2}} + {{h_{12}}^{2}{x_{2}}^{2}} + {h_{11}^{*}h_{12}x_{2}x_{1}^{*}} + {h_{12}^{*}h_{11}x_{1}x_{2}^{*}}} \right)^{j\theta}}} \\{= {\left( {{{h_{11}}^{2}{x_{1}}^{2}} + {{h_{12}}^{2}{x_{2}}^{2}} + {2\mspace{14mu} R\; e\mspace{11mu} \left\{ {\left( {h_{11}^{*}h_{12}} \right)x_{2}x_{1}^{*}} \right\}}} \right)^{j\theta}}} \\{= {C\; {^{j\theta}.}}}\end{matrix} & (14)\end{matrix}$

Since in equation (14), “x₁′x₁*+x₂′x₂*” and C (equals to(|h₁₁|²|x₁|²+|h₁₂|²|x₂|²+2Re{h₁₁*h₁₂x₂x₁*})) are known, the phase errorθ can be accurately calculated.

Please refer to FIG. 4. FIG. 4 is a flowchart illustrating a method 400for estimating phase error according to a second embodiment of thepresent invention. The steps are described as follows:

Step 401: Executing Hermitian transpose on the channel coefficientmatrix H for generating a Hermitian-transposed channel coefficientmatrix H_(A);

Step 402: Multiplying the Hermitian-transposed channel coefficientmatrix H_(A) with the channel coefficient matrix H for generating aproduct channel coefficient matrix H_(B);

Step 403: Inversing the product channel coefficient matrix H_(B) forgenerating an inversed product channel coefficient matrix H_(C);

Step 404: Adding a real constant Z to each of the elements on thediagonal of the inversed product channel coefficient matrix H_(C) forgenerating constant-added inversed product channel coefficient matrixH_(D);

Step 405: Multiplying the constant-added inversed product channelcoefficient matrix H_(D) with the Hermitian-transposed channelcoefficient matrix H_(A) for generating a diversity gain matrix G_(D);and

Step 406: Generating the phase error θ according to the diversity gainmatrix G_(D), the received signal matrix Y, and the pilot signal matrixX.

The method 400 for estimating the phase error θ is similar to theconventional method, and the difference is that in steps 404, a realconstant Z is added to each of the elements on diagonal of the inversedproduct channel coefficient matrix H_(C). In this way, the value of thegain of the diversity gain matrix G_(D) can be increased. Furthermore,if the real constant Z is large enough, then the value of the gain ofthe diversity gain matrix G_(D) is large enough as well so that in theequation (6), the noise matrix can be ignored. Therefore, the estimatedphase error θ generated by the method 400 can be much more accurate thanthe phase error θ estimated by the conventional method.

The following description is an exemplary embodiment illustrating usingthe method 400 to estimate the phase error θ. Assuming the number of thetransmitting antennas T_(X) is 2, and the number of the receivingantennas R_(X) is 2 (a 2T2R OFDM communications system), therefore, thereceived signal y (after being fast Fourier transformed) can be derivedfrom the following equations:

$\begin{matrix}{{Y_{21} = {\begin{pmatrix}y_{1} \\y_{2}\end{pmatrix} = {{{H_{22} \cdot X_{21}} + N_{21}} = {{\begin{pmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{pmatrix}\begin{pmatrix}{x_{1}^{j\theta}} \\{x_{2}^{j\theta}}\end{pmatrix}} + \begin{pmatrix}n_{1} \\n_{2}\end{pmatrix}}}}};} & (8)\end{matrix}$

where Y_(2×1) represents the received signal matrix after being fastFourier transformed, H_(2×2) represents the channel coefficient matrix,X_(2×1) represents the pilot signal matrix, and N_(2×1) represents thenoise matrix. According to steps 401˜405, the diversity gain matrixG_(D) can be obtained by the following equation:

$\begin{matrix}\begin{matrix}{G_{D} = {\left( {H^{H}H} \right)_{Z}^{- 1}H^{H}}} \\{= {{\left( {H\; {1 \cdot H}} \right)_{Z}^{- 1} \cdot H}\; 1}} \\{= {\left\lbrack {\begin{pmatrix}h_{11}^{*} & h_{21}^{*} \\h_{12}^{*} & h_{22}^{*}\end{pmatrix}\begin{pmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{pmatrix}} \right\rbrack_{Z}^{- 1}\begin{pmatrix}h_{11}^{*} & h_{21}^{*} \\h_{12}^{*} & h_{22}^{*}\end{pmatrix}}} \\{= \begin{pmatrix}{{h_{11}{^{2}{{+ {h_{21}}^{2}} + Z}}}} & {{h_{11}^{*}h_{12}} + {h_{21}^{*}h_{22}}} \\{{h_{12}^{*}h_{11}} + {h_{22}^{*}h_{21}}} & \left| {h_{12}{^{2}{{+ {h_{22}}^{2}} + Z}}} \right.\end{pmatrix}^{- 1}} \\{{{\begin{pmatrix}h_{11}^{*} & h_{21}^{*} \\h_{12}^{*} & h_{22}^{*}\end{pmatrix} = {\frac{1}{K}\begin{pmatrix}P & S \\R & Q\end{pmatrix}}};}}\end{matrix} & (15)\end{matrix}$

Where K equals|h₁₁|²|h₂₂|²+|h₁₂|²|h₂₁|²+Z(|h₁₁|²+|h₁₂|²+|h₂₁|²|h₂₂|²)+Z²+h₁₁h₂₂h₁₂*h₂₁*+h₁₁*h₂₂*h₁₂h₂₁,P equals (|h₂₂|²+Z)h₁₁*−h₁₂*h₂₁*h₂₂, Q equals(|h₁₁|²+Z)h₂₂*−h₂₁*h₁₂*h₁₁, R equals (|h₂₁|²+Z)h₁₂*−h₁₁*h₂₂*h₂₁, and Sequals (|h₁₂|²+Z)h₂₁*−h₁₁*h₂₂*h₁₂. If the real constant Z is largeenough, the diversity gain matrix G_(D) can be further derived as thefollowing equation:

$\begin{matrix}{{G_{D} \approx {\frac{1}{Z^{2}}\begin{pmatrix}{{Zh}_{11}^{*} - {h_{12}^{*}h_{21}^{*}h_{22}}} & {{Zh}_{21}^{*} - {h_{11}^{*}h_{22}^{*}h_{12}}} \\{{Zh}_{12}^{*} - {h_{11}^{*}h_{22}^{*}h_{21}}} & {{Zh}_{22}^{*} - {h_{12}^{*}h_{21}^{*}h_{11}}}\end{pmatrix}} \approx {\frac{1}{Z}\begin{pmatrix}h_{11}^{*} & h_{21}^{*} \\h_{12}^{*} & h_{22}^{*}\end{pmatrix}}};} & (16)\end{matrix}$

where the gain of the diversity gain matrix G_(D) according to theequation (16) is large enough to ignore the noise.

Additionally, the value of the real constant Z can be defined as thefollowing equation for being large enough:

$\begin{matrix}{{Z \geq {100 \cdot {{Max}\left( {{\sum\limits_{i = 1}^{N_{R}}{h_{i1}}^{2}},{\sum\limits_{i = 1}^{N_{R}}{h_{i\; 2}}^{2}},...\mspace{11mu},\mspace{11mu} {\sum\limits_{i = 1}^{N_{R}}{h_{{iN}_{r}}}^{2}}} \right)}}};} & (17)\end{matrix}$

where N_(R) represents the number of the receiving antennas, and N_(T)represents the number of the transmitting antennas.

Furthermore, in the MIMO OFDM communications system 200 of the presentinvention, the space-time-frequency processing device 112 can choosedifferent schemes, such as Space-Division Multiplexing (SDM), Space-TimeBlock Coding (STBC), or hybrid STBC-SDM modes, and the methods 300 and400 are applicable to different space-time frequency processing schemes.

To sum up, the present invention provides method for efficientlyestimating phase error in the MIMO OFDM system, and allows that thenumber of the receiving antennas can be less than the number of thetransmitting antennas. In other words, there is no constraint on thenumbers of the transmitting and receiving antennas, which provides greatconvenience. Furthermore, the method of the present invention can beapplicable to different space-time-frequency processing schemes, whichreduces cost.

Those skilled in the art will readily observe that numerousmodifications and alterations of the device and method may be made whileretaining the teachings of the invention. Accordingly, the abovedisclosure should be construed as limited only by the metes and boundsof the appended claims.

1. A receiver of a Multiple Input Multiple Output (MIMO) OrthogonalFrequency Division Multiplexing (OFDM) communications system, thereceiver comprising: means for executing Hermitian transpose on achannel coefficient matrix of the MIMO OFDM communications system forgenerating a Hermitian-transposed channel coefficient matrix; means formultiplying the Hermitian-transposed channel coefficient matrix with thechannel coefficient matrix for generating a product channel coefficientmatrix; means for adding a real constant to each element on diagonal ofthe product channel coefficient matrix for generating a constant-addedproduct channel coefficient matrix; means for inversing theconstant-added product channel coefficient matrix for generating aninversed constant-added product channel coefficient matrix; means formultiplying the inversed constant-added product channel coefficientmatrix with the Hermitian-transposed channel coefficient matrix forgenerating a diversity gain matrix; and means for generating the phaseerror according to the diversity gain matrix, a received signal matrix,and a pilot signal matrix.
 2. The receiver of claim 1, furthercomprising: means for converting radio frequency signals to digitalsignals; and means for fast Fourier transforming the digital signals asthe received signal matrix.
 3. The receiver of claim 2, wherein meansfor converting the radio frequency signals to digital signals comprises:means for down-converting the radio frequency signals to analog signals;and means for converting the analog signals to the digital signals. 4.The receiver of claim 1, wherein each element in the channel coefficientmatrix represents a channel coefficient between one transmitting antennaand one receiving antenna of the MIMO OFDM communications system.
 5. Thereceiver of claim 1, wherein each element in the received signal matrixrepresents a received signal of one receiving antenna of the MIMO OFDMcommunications system, and each element in the pilot signal matrixrepresent a pilot signal contained in a received signal.
 6. The receiverof claim 1, wherein a value of the real constant is defined as thefollowing equation:${Z \geq {100 \cdot {{Max}\left( {{\sum\limits_{i = 1}^{N_{R}}{h_{i1}}^{2}},{\sum\limits_{i = 1}^{N_{R}}{h_{i\; 2}}^{2}},...\mspace{11mu},\mspace{11mu} {\sum\limits_{i = 1}^{N_{R}}{h_{{iN}_{r}}}^{2}}} \right)}}};$wherein Z represents the real constant, N_(R) represents a number of thereceiving antennas, N_(T) represents a number of the transmittingantennas, and h_(ij) represents a channel coefficient between onetransmitting antenna and one receiving antenna of the MIMO OFDMcommunications system.
 7. A method for estimating a phase error in areceiver of a MIMO OFDM communications system, the method comprising:executing Hermitian transpose on a channel coefficient matrix of theMIMO OFDM communications system for generating a Hermitian-transposedchannel coefficient matrix; multiplying the Hermitian-transposed channelcoefficient matrix with the channel coefficient matrix for generating aproduct channel coefficient matrix; adding a real constant to eachelement on diagonal of the product channel coefficient matrix forgenerating a constant-added product channel coefficient matrix;inversing the constant-added product channel coefficient matrix forgenerating an inversed constant-added product channel coefficientmatrix; multiplying the inversed constant-added product channelcoefficient matrix with the Hermitian-transposed channel coefficientmatrix for generating a diversity gain matrix; and generating the phaseerror according to the diversity gain matrix, a received signal matrix,and a pilot signal matrix.
 8. The method of claim 7, further comprising:converting radio frequency signals to digital signals; and fast Fouriertransforming the digital signals as the received signal matrix.
 9. Themethod of claim 8, wherein converting the radio frequency signals todigital signals comprises: down-converting the radio frequency signalsto analog signals; and converting the analog signals to the digitalsignals.
 10. The method of claim 7, wherein each element in the channelcoefficient matrix represents a channel coefficient between onetransmitting antenna and one receiving antenna of the MIMO OFDMcommunications system.
 11. The method of claim 7, wherein each elementin the received signal matrix represents a received signal of onereceiving antenna of the MIMO OFDM communications system, and eachelement in the pilot signal matrix represent a pilot signal contained ina received signal.
 12. The method of claim 7, wherein a value of thereal constant is defined as the following equation:${Z \geq {100 \cdot {{Max}\left( {{\sum\limits_{i = 1}^{N_{R}}{h_{i1}}^{2}},{\sum\limits_{i = 1}^{N_{R}}{h_{i\; 2}}^{2}},...\mspace{11mu},{\underset{i = 1}{\overset{N_{R}}{\mspace{11mu}\sum}}{h_{{iN}_{T}}}^{2}}} \right)}}};$wherein Z represents the real constant, N_(R) represents a number of thereceiving antennas, N_(T) represents a number of the transmittingantennas, and h_(ij) represents a channel coefficient between onetransmitting antenna and one receiving antenna of the MIMO OFDMcommunications system.